Evolution by pseudomonotone or weakly continuous mappings

Abstract

As already advertised in the previous Chapter 7, evolution problems involve one variable, a time t, having a certain specific character and thus a specific treatment is useful, although some methods (applicable under special circumstances, see Sections 8.9 and 8.10) can wipe this specific character off. Conventional methods we will scrutinize in this chapter deal with this one-dimensional variable t by two ways:

(i) discretize t, and then thus created auxiliary approximate problems are based on our knowledge from Part I,

(ii) keep t continuous but approximate the rest by a Galerkin method similarly as we did in Section 2.1, and then the approximate problems are based on ordinary differential equations and Section 1.6.